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A272225 Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 443", based on the 5-celled von Neumann neighborhood. 4
1, 5, 13, 40, 25, 97, 72, 189, 77, 324, 113, 457, 184, 593, 337, 800, 305, 1132, 297, 1381, 408, 1625, 584, 1933, 709, 2288, 785, 2660, 1033, 2961, 1316, 3421, 1372, 3937, 1409, 4436, 1525, 4965, 1620, 5553, 1805, 6084, 1957, 6689, 2236, 7181, 2752, 7689 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Initialized with a single black (ON) cell at stage zero.

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

LINKS

Robert Price, Table of n, a(n) for n = 0..128

Robert Price, Diagrams of the first 20 stages

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to 2D 5-Neighbor Cellular Automata

Index to Elementary Cellular Automata

MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=443; stages=128;

rule=IntegerDigits[code, 2, 10];

g=2*stages+1; (* Maximum size of grid *)

a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)

ca=a;

ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];

PrependTo[ca, a];

(* Trim full grid to reflect growth by one cell at each stage *)

k=(Length[ca[[1]]]+1)/2;

ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];

Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)

CROSSREFS

Sequence in context: A080143 A077919 A295913 * A272585 A026069 A054856

Adjacent sequences:  A272222 A272223 A272224 * A272226 A272227 A272228

KEYWORD

nonn,easy

AUTHOR

Robert Price, Apr 22 2016

STATUS

approved

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Last modified April 1 14:52 EDT 2020. Contains 333163 sequences. (Running on oeis4.)